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Pythagorean Theorem proof

By |2018-04-23T14:19:10-07:00September 25th, 2017|Greeks, Math|

A right triangle. This is the proof of the Pythagorean Theorem supposedly written by Pythagoras about 500 BC: The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2. Try it yourself: if Side [...]

Science in Early Modern Europe

By |2018-04-13T01:12:09-07:00August 7th, 2017|Modern Europe, Science|

Early modern science: Tycho Brahe (He looks funny because his nose got cut off in a duel and he wore a false one made of brass.) New observatories in Europe Europe's colonialism and slave trading brought a lot of money to Europe. By 1600 AD the fashion for building new observatories that had swept from China west [...]

René Descartes – European philosophy

By |2019-05-06T07:44:32-07:00August 6th, 2017|Modern Europe, Philosophy|

René Descartes Who was Descartes? René Descartes was one of the earliest philosophers of the European Enlightenment, in the early 1600s AD. He was just 8 years younger than Hobbes. While Descartes was growing up, Henry IV was killed, Marie de Medici ruled, and then Richelieu. More about Hobbes The Enlightenment All our European History [...]

Medieval science in Europe

By |2018-04-24T09:01:17-07:00August 4th, 2017|Medieval, Science|

Medieval science: an Italian pharmacy jar, about 1400 AD (Metropolitan Museum, New York) Learning from Islamic science During the Middle Ages, the best scientists and doctors weren't in Europe. They were in the Islamic Empire to the south and east. Most of the science and medicine that people were doing in Europe was learning from Islamic scientists [...]

What is area? Simple geometry

By |2017-07-29T13:29:39-07:00July 29th, 2017|Math|

Calculating the area of your room. The area of a room is the size of the floor. Suppose you wanted to find out whether your room was really bigger than your brother's room. You'll need to measure your room, and his room. Suppose your room is ten feet long and fifteen feet wide, [...]

What is a trapezoid? Simple geometry

By |2017-07-29T13:16:13-07:00July 29th, 2017|Math|

This is a trapezoid. A trapezoid is a kind of quadrilateral that has at least two sides that are parallel to each other. A parallelogram is a trapezoid that has two pairs of parallel sides, and a rhombus is a special kind of parallelogram, and so are rectangles and squares. To figure out the perimeter of a trapezoid, you can add the lengths of [...]

What is a square? Simple geometry

By |2018-04-23T16:01:49-07:00July 29th, 2017|Math|

This is a square. The darker purple line is the perimeter of the square. A square is a flat shape, in one plane, defined by four points at the four corners. A square has four sides all of equal length, and four corners, all right angles (90 degree angles). So a square is a kind of rectangle. To figure [...]

Area of a sphere – Volume of a sphere

By |2017-07-29T13:10:50-07:00July 29th, 2017|Math|

This is a sphere. A sphere is a three-dimensional circle. Or you could say that a sphere is the set of all the points that are at the same distance from the center of the sphere. In nature, centrifugal force and gravity tend to make a lot of things into spheres: soap bubbles, for instance, atoms, and planets. The radius of a sphere [...]